Question

Match List-I with List-II.
\begin{array}{|c|c|c|} \hline \text{List-I} & & \text{List-II} \\\ \hline \text{A. Coefficient of viscosity} & & \text{I.} \; [M L^2 T^{-2}] \\\ \text{B. Surface Tension} & & \text{II.} \; [M L^2 T^{-1}] \\\ \text{C. Angular momentum} & & \text{III.} \; [M L^1 T^{-1}] \\\ \text{D. Rotational kinetic energy} & & \text{IV.} \; [M L^0 T^{-2}] \\\ \hline \end{array}

• A. A–II, B–I, C–IV, D–III
• B. A–I, B–II, C–III, D–IV
• C. A–III, B–IV, C–II, D–I
• D. A–IV, B–III, C–II, D–I

Answer 1

Answer: (C)

A–III, B–IV, C–II, D–I

Answer 2

Use dimensional analysis:

Coefficient of viscosity $\eta = \frac{F}{A} \frac{dy}{dt} \Rightarrow [\eta] = [ML^{-1}T^{-1}]$.

Surface Tension $S.T = \frac{F}{L} \Rightarrow [ML^{0}T^{-2}]$.

Angular momentum $L = mvr \Rightarrow [ML^{2}T^{-1}]$.

Rotational kinetic energy $K.E. = \frac{1}{2} I \omega^2 \Rightarrow [ML^{2}T^{-2}]$.

This confirms the matching as $A - III$, $B - IV$, $C - II$, $D - I$.